class IndependentMultivariateOLSTests(unittest.TestCase):
@classmethod
def setUpClass(cls):
np.random.seed(0)
cls.X = np.random.normal(size=(1000, 1))
cls.Y = np.random.normal(size=(cls.X.shape[0], 2))
def test_ols(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.X, self.Y)
# coefficient
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.02924966, -0.03484827],
[-0.00978688, 0.00336316]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.stderr,
np.array([[0.03083908, 0.03121143], [0.03002101,
0.03038348]]).reshape(2, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185,
0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.X, self.Y),
-2758.54387369,
places=3)
# to_json
json_dict = self.model.to_json(
'./tests/linear_models/OLS/MultivariateOLS/')
self.assertEqual(json_dict['properties']['solver'], 'pinv')
# from_json
self.model_from_json = OLS.from_json(json_dict)
np.testing.assert_array_almost_equal(self.model.coef,
self.model_from_json.coef,
decimal=3)
np.testing.assert_array_almost_equal(self.model.stderr,
self.model_from_json.stderr,
decimal=3)
np.testing.assert_array_almost_equal(self.model.dispersion,
self.model_from_json.dispersion,
decimal=3)
def test_ols_l2_regularized(self):
self.model = OLS(solver='auto',
fit_intercept=True,
est_stderr=True,
reg_method='l2',
alpha=0.1,
l1_ratio=1,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.X, self.Y)
# coefficient
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.0292465, -0.03484456], [-0.00978591,
0.00336286]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertTrue(self.model.stderr is None)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185,
0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.X, self.Y),
-2758.5438737,
places=3)
def test_ols_l1_regularized(self):
# sklearn l1 and elstic net does not support sample weight
pass
def test_ols_sample_weight_all_half(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.X, self.Y, sample_weight=0.5)
# coefficient
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.02924966, -0.03484827],
[-0.00978688, 0.00336316]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.stderr,
np.array([[0.03083908, 0.03121143], [0.03002101,
0.03038348]]).reshape(2, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185,
0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.X, self.Y, 0.5),
old_div(-2758.54387369, 2.),
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.X, self.Y).shape, (1000, ))
def test_ols_sample_weight_all_zero(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.assertRaises(ValueError, self.model.fit, self.X, self.Y, 0)
def test_ols_sample_weight_half_zero_half_one(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
len_half = 500
self.model.fit(self.X,
self.Y,
sample_weight=np.array([1] * len_half + [0] *
(self.X.shape[0] - len_half)))
self.model_half = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model_half.fit(self.X[:len_half], self.Y[:len_half])
# coefficient
np.testing.assert_array_almost_equal(self.model.coef,
self.model_half.coef,
decimal=3)
# std.err
np.testing.assert_array_almost_equal(self.model.stderr,
self.model_half.stderr,
decimal=3)
# scale
np.testing.assert_array_almost_equal(self.model.dispersion,
self.model_half.dispersion,
decimal=3)
# corner cases
def test_ols_one_data_point(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.X[0:1, :], self.Y[0:1, ], sample_weight=0.5)
# coef
self.assertEqual(self.model.coef.shape, (2, 2))
# scale
np.testing.assert_array_almost_equal(self.model.dispersion,
np.array([[0, 0], [0, 0]]),
decimal=6)
# loglike_per_sample
np.testing.assert_array_equal(
self.model.loglike_per_sample(self.X[0:1, :], self.Y[0:1, ]),
np.array([0]))
np.testing.assert_array_almost_equal(
self.model.loglike_per_sample(
np.array(self.X[0:1, :].tolist() * 6),
np.array([
self.Y[0, ], self.Y[1, ], self.Y[0, ], self.Y[1, ],
self.Y[1, ], self.Y[0, ]
])),
np.array([0, -np.Infinity, 0, -np.Infinity, -np.Infinity, 0]),
decimal=3)
def test_ols_multicolinearty(self):
self.model_col = OLS(solver='pinv',
fit_intercept=False,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
X = np.hstack([self.X[:, 0:1], self.X[:, 0:1]])
self.model_col.fit(X, self.Y, sample_weight=0.5)
self.model = OLS(solver='pinv',
fit_intercept=False,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.X[:, 0:1], self.Y, sample_weight=0.5)
# stderr
self.assertEqual(self.model_col.stderr, None)
# scale
np.testing.assert_array_almost_equal(self.model_col.dispersion,
self.model.dispersion,
decimal=3)
# loglike_per_sample
np.testing.assert_array_almost_equal(
self.model_col.loglike_per_sample(X, self.Y),
self.model.loglike_per_sample(self.X[:, 0:1], self.Y),
decimal=0)
np.testing.assert_array_almost_equal(self.model_col.predict(X),
self.model.predict(self.X[:,
0:1]),
decimal=1)
class UnivariateOLSTests(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.data_longley = sm.datasets.longley.load()
def test_ols(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.data_longley.exog, self.data_longley.endog)
# coefficient
self.assertEqual(self.model.coef.shape, (1, 7))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([-3482258.63459582, 15.0618722713733, -0.358191792925910E-01,
-2.02022980381683, -1.03322686717359, -0.511041056535807E-01,
1829.15146461355]).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (1, 7))
np.testing.assert_array_almost_equal(
old_div(self.model.stderr, np.sqrt(old_div(9., self.data_longley.exog.shape[0]))),
np.array([890420.383607373, 84.9149257747669, 0.03349,
0.488399681651699, 0.214274163161675, 0.226073200069370,
455.478499142212]).reshape(1, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (1, 1))
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion, (old_div(9., self.data_longley.exog.shape[0]))),
np.array([[92936.0061673238]]),
decimal=3)
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) - self.model.predict(self.data_longley.exog),
np.array([267.34003, -94.01394, 46.28717, -410.11462,
309.71459, -249.31122, -164.04896, -13.18036, 14.30477, 455.39409,
-17.26893, -39.05504, -155.54997, -85.67131, 341.93151,
-206.75783]).reshape(-1, 1),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.data_longley.exog, self.data_longley.endog),
-109.61743480849013,
places=3)
# to_json
json_dict = self.model.to_json('./tests/linear_models/OLS/UnivariateOLS/')
self.assertEqual(json_dict['properties']['solver'], 'pinv')
# from_json
self.model_from_json = OLS.from_json(json_dict)
np.testing.assert_array_almost_equal(
self.model.coef,
self.model_from_json.coef,
decimal=3)
np.testing.assert_array_almost_equal(
self.model.stderr,
self.model_from_json.stderr,
decimal=3)
self.assertEqual(
self.model.dispersion,
self.model_from_json.dispersion)
def test_ols_l1_regularized(self):
# sklearn elastic net and l1 does not take sample_weights, will not test
pass
def test_ols_l2_regularized(self):
# there is a bug in sklearn with weights, it can only use list right now
self.model = OLS(
solver='auto', fit_intercept=True, est_stderr=True,
reg_method='l2', alpha=0.1, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.data_longley.exog, self.data_longley.endog, sample_weight=0.5)
# coefficient
print(self.model.coef)
print(self.model.dispersion)
print(self.data_longley.endog.reshape(-1, 1) - self.model.predict(self.data_longley.exog))
print(self.model.loglike(self.data_longley.exog, self.data_longley.endog))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([-2.0172203, -52.14364269, 0.07089677, -0.42552125,
-0.57305292, -0.41272483, 48.32484052]).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertTrue(self.model.stderr is None)
# scale
self.assertEqual(self.model.dispersion.shape, (1, 1))
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion, (old_div(9., self.data_longley.exog.shape[0]))),
np.array([[250870.081]]),
decimal=3)
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) - self.model.predict(self.data_longley.exog),
np.array([[280.31871146],
[-131.6981265],
[90.64414685],
[-400.10244445],
[-440.59604167],
[-543.88595187],
[200.70483416],
[215.88629903],
[74.9456573],
[913.85128645],
[424.15996133],
[-9.5797488],
[-360.96841852],
[27.214226],
[150.87705909],
[-492.17489392]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.data_longley.exog, self.data_longley.endog),
-117.561627187,
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.data_longley.exog, self.data_longley.endog).shape,
(16, ))
def test_ols_elastic_net_regularized(self):
# sklearn elastic net and l1 does not take sample_weights, will not test
pass
def test_ols_sample_weight_all_half(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.data_longley.exog, self.data_longley.endog, sample_weight=0.5)
# coefficient
np.testing.assert_array_almost_equal(
self.model.coef,
np.array((-3482258.63459582, 15.0618722713733, -0.358191792925910E-01,
-2.02022980381683, -1.03322686717359, -0.511041056535807E-01,
1829.15146461355)).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
np.testing.assert_array_almost_equal(
old_div(self.model.stderr, np.sqrt(old_div(9., self.data_longley.exog.shape[0]))),
np.array((890420.383607373, 84.9149257747669, 0.334910077722432E-01,
0.488399681651699, 0.214274163161675, 0.226073200069370,
455.478499142212)).reshape(1, -1),
decimal=1)
# scale
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion, (old_div(9., self.data_longley.exog.shape[0]))),
np.array((92936.0061673238)))
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) - self.model.predict(self.data_longley.exog),
np.array((267.34003, -94.01394, 46.28717, -410.11462,
309.71459, -249.31122, -164.04896, -13.18036, 14.30477, 455.39409,
-17.26893, -39.05504, -155.54997, -85.67131, 341.93151,
-206.75783)).reshape(-1, 1),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.data_longley.exog, self.data_longley.endog),
-109.61743480849013,
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.data_longley.exog, self.data_longley.endog).shape,
(16, ))
def test_ols_sample_weight_all_zero(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.assertRaises(ValueError, self.model.fit,
self.data_longley.exog, self.data_longley.endog, 0)
def test_ols_sample_weight_half_zero_half_one(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
len_half = 8
self.model.fit(self.data_longley.exog, self.data_longley.endog,
sample_weight=np.array([1] * len_half +
[0] * (self.data_longley.exog.shape[0] - len_half)))
self.model_half = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model_half.fit(self.data_longley.exog[:len_half], self.data_longley.endog[:len_half])
# coefficient
np.testing.assert_array_almost_equal(
self.model.coef,
self.model_half.coef,
decimal=3)
# std.err
np.testing.assert_array_almost_equal(
self.model.stderr,
self.model_half.stderr,
decimal=3)
# scale
np.testing.assert_array_almost_equal(
self.model.dispersion,
self.model_half.dispersion,
decimal=3)
# corner cases
def test_ols_one_data_point(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.data_longley.exog[0:1, :],
self.data_longley.endog[0:1, ], sample_weight=0.5)
# coef
self.assertEqual(self.model.coef.shape, (1, 7))
# scale
np.testing.assert_array_almost_equal(self.model.dispersion, np.array([[0]]))
# loglike_per_sample
np.testing.assert_array_equal(self.model.loglike_per_sample(
self.data_longley.exog[0:1, :], self.data_longley.endog[0:1, ]), np.array([0]))
np.testing.assert_array_almost_equal(self.model.loglike_per_sample(
np.array(self.data_longley.exog[0:1, :].tolist() * 6),
np.array([60323, 0, 60323, 60322, 60322, 60323])),
np.array([0, -np.Infinity, 0, -np.Infinity, -np.Infinity, 0]), decimal=3)
def test_ols_multicolinearty(self):
self.model_col = OLS(
solver='pinv', fit_intercept=False, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
X = np.hstack([self.data_longley.exog[:, 0:1], self.data_longley.exog[:, 0:1]])
self.model_col.fit(X,
self.data_longley.endog, sample_weight=0.8)
self.model = OLS(
solver='pinv', fit_intercept=False, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.data_longley.exog[:, 0:1],
self.data_longley.endog, sample_weight=0.8)
# coef
np.testing.assert_array_almost_equal(
self.model_col.coef, np.array([319.47969664, 319.47969664]).reshape(1, -1), decimal=3)
# stderr
self.assertEqual(self.model_col.stderr, None)
# scale
np.testing.assert_array_almost_equal(
self.model_col.dispersion, self.model.dispersion, decimal=3)
# loglike_per_sample
np.testing.assert_array_almost_equal(
self.model_col.loglike_per_sample(X, self.data_longley.endog),
self.model.loglike_per_sample(self.data_longley.exog[:, 0:1],
self.data_longley.endog), decimal=3)
np.testing.assert_array_almost_equal(
self.model_col.predict(X),
self.model.predict(self.data_longley.exog[:, 0:1]), decimal=3)
class UnivariateOLSTests(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.data_longley = sm.datasets.longley.load()
def test_ols(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.data_longley.exog, self.data_longley.endog)
# coefficient
self.assertEqual(self.model.coef.shape, (1, 7))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([
-3482258.63459582, 15.0618722713733, -0.358191792925910E-01,
-2.02022980381683, -1.03322686717359, -0.511041056535807E-01,
1829.15146461355
]).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (1, 7))
np.testing.assert_array_almost_equal(
old_div(self.model.stderr,
np.sqrt(old_div(9., self.data_longley.exog.shape[0]))),
np.array([
890420.383607373, 84.9149257747669, 0.03349, 0.488399681651699,
0.214274163161675, 0.226073200069370, 455.478499142212
]).reshape(1, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (1, 1))
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion,
(old_div(9., self.data_longley.exog.shape[0]))),
np.array([[92936.0061673238]]),
decimal=3)
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) -
self.model.predict(self.data_longley.exog),
np.array([
267.34003, -94.01394, 46.28717, -410.11462, 309.71459,
-249.31122, -164.04896, -13.18036, 14.30477, 455.39409,
-17.26893, -39.05504, -155.54997, -85.67131, 341.93151,
-206.75783
]).reshape(-1, 1),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.data_longley.exog,
self.data_longley.endog),
-109.61743480849013,
places=3)
# to_json
json_dict = self.model.to_json(
'./tests/linear_models/OLS/UnivariateOLS/')
self.assertEqual(json_dict['properties']['solver'], 'pinv')
# from_json
self.model_from_json = OLS.from_json(json_dict)
np.testing.assert_array_almost_equal(self.model.coef,
self.model_from_json.coef,
decimal=3)
np.testing.assert_array_almost_equal(self.model.stderr,
self.model_from_json.stderr,
decimal=3)
self.assertEqual(self.model.dispersion,
self.model_from_json.dispersion)
def test_ols_l1_regularized(self):
# sklearn elastic net and l1 does not take sample_weights, will not test
pass
def test_ols_l2_regularized(self):
# there is a bug in sklearn with weights, it can only use list right now
self.model = OLS(solver='auto',
fit_intercept=True,
est_stderr=True,
reg_method='l2',
alpha=0.1,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.data_longley.exog,
self.data_longley.endog,
sample_weight=0.5)
# coefficient
np.testing.assert_array_almost_equal(self.model.coef,
np.array([
-2.0172203, -52.14364269,
0.07089677, -0.42552125,
-0.57305292, -0.41272483,
48.32484052
]).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertTrue(self.model.stderr is None)
# scale
self.assertEqual(self.model.dispersion.shape, (1, 1))
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion,
(old_div(9., self.data_longley.exog.shape[0]))),
np.array([[250870.081]]),
decimal=3)
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) -
self.model.predict(self.data_longley.exog),
np.array([[280.31871146], [-131.6981265], [90.64414685],
[-400.10244445], [-440.59604167], [-543.88595187],
[200.70483416], [215.88629903], [74.9456573],
[913.85128645], [424.15996133], [-9.5797488],
[-360.96841852], [27.214226], [150.87705909],
[-492.17489392]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.data_longley.exog,
self.data_longley.endog),
-117.561627187,
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.data_longley.exog,
self.data_longley.endog).shape,
(16, ))
def test_ols_elastic_net_regularized(self):
# sklearn elastic net and l1 does not take sample_weights, will not test
pass
def test_ols_sample_weight_all_half(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.data_longley.exog,
self.data_longley.endog,
sample_weight=0.5)
# coefficient
np.testing.assert_array_almost_equal(
self.model.coef,
np.array(
(-3482258.63459582, 15.0618722713733, -0.358191792925910E-01,
-2.02022980381683, -1.03322686717359, -0.511041056535807E-01,
1829.15146461355)).reshape(1, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
np.testing.assert_array_almost_equal(
old_div(self.model.stderr,
np.sqrt(old_div(9., self.data_longley.exog.shape[0]))),
np.array(
(890420.383607373, 84.9149257747669, 0.334910077722432E-01,
0.488399681651699, 0.214274163161675, 0.226073200069370,
455.478499142212)).reshape(1, -1),
decimal=1)
# scale
np.testing.assert_array_almost_equal(
old_div(self.model.dispersion,
(old_div(9., self.data_longley.exog.shape[0]))),
np.array((92936.0061673238)))
# predict
np.testing.assert_array_almost_equal(
self.data_longley.endog.reshape(-1, 1) -
self.model.predict(self.data_longley.exog),
np.array((267.34003, -94.01394, 46.28717, -410.11462, 309.71459,
-249.31122, -164.04896, -13.18036, 14.30477, 455.39409,
-17.26893, -39.05504, -155.54997, -85.67131, 341.93151,
-206.75783)).reshape(-1, 1),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(self.model.loglike(self.data_longley.exog,
self.data_longley.endog),
-109.61743480849013,
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.data_longley.exog,
self.data_longley.endog).shape,
(16, ))
def test_ols_sample_weight_all_zero(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.assertRaises(ValueError, self.model.fit, self.data_longley.exog,
self.data_longley.endog, 0)
def test_ols_sample_weight_half_zero_half_one(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
len_half = 8
self.model.fit(self.data_longley.exog,
self.data_longley.endog,
sample_weight=np.array(
[1] * len_half + [0] *
(self.data_longley.exog.shape[0] - len_half)))
self.model_half = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model_half.fit(self.data_longley.exog[:len_half],
self.data_longley.endog[:len_half])
# coefficient
np.testing.assert_array_almost_equal(self.model.coef,
self.model_half.coef,
decimal=3)
# std.err
np.testing.assert_array_almost_equal(self.model.stderr,
self.model_half.stderr,
decimal=3)
# scale
np.testing.assert_array_almost_equal(self.model.dispersion,
self.model_half.dispersion,
decimal=3)
# corner cases
def test_ols_one_data_point(self):
self.model = OLS(solver='pinv',
fit_intercept=True,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.data_longley.exog[0:1, :],
self.data_longley.endog[0:1, ],
sample_weight=0.5)
# coef
self.assertEqual(self.model.coef.shape, (1, 7))
# scale
np.testing.assert_array_almost_equal(self.model.dispersion,
np.array([[0]]))
# loglike_per_sample
np.testing.assert_array_equal(
self.model.loglike_per_sample(self.data_longley.exog[0:1, :],
self.data_longley.endog[0:1, ]),
np.array([0]))
np.testing.assert_array_almost_equal(
self.model.loglike_per_sample(
np.array(self.data_longley.exog[0:1, :].tolist() * 6),
np.array([60323, 0, 60323, 60322, 60322, 60323])),
np.array([0, -np.Infinity, 0, -np.Infinity, -np.Infinity, 0]),
decimal=3)
def test_ols_multicolinearty(self):
self.model_col = OLS(solver='pinv',
fit_intercept=False,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
X = np.hstack(
[self.data_longley.exog[:, 0:1], self.data_longley.exog[:, 0:1]])
self.model_col.fit(X, self.data_longley.endog, sample_weight=0.8)
self.model = OLS(solver='pinv',
fit_intercept=False,
est_stderr=True,
reg_method=None,
alpha=0,
l1_ratio=0,
tol=1e-4,
max_iter=100,
coef=None,
stderr=None,
dispersion=None)
self.model.fit(self.data_longley.exog[:, 0:1],
self.data_longley.endog,
sample_weight=0.8)
# coef
np.testing.assert_array_almost_equal(
self.model_col.coef,
np.array([319.47969664, 319.47969664]).reshape(1, -1),
decimal=3)
# stderr
self.assertEqual(self.model_col.stderr, None)
# scale
np.testing.assert_array_almost_equal(self.model_col.dispersion,
self.model.dispersion,
decimal=3)
# loglike_per_sample
np.testing.assert_array_almost_equal(
self.model_col.loglike_per_sample(X, self.data_longley.endog),
self.model.loglike_per_sample(self.data_longley.exog[:, 0:1],
self.data_longley.endog),
decimal=3)
np.testing.assert_array_almost_equal(
self.model_col.predict(X),
self.model.predict(self.data_longley.exog[:, 0:1]),
decimal=3)
class IndependentMultivariateOLSTests(unittest.TestCase):
@classmethod
def setUpClass(cls):
np.random.seed(0)
cls.X = np.random.normal(size=(1000, 1))
cls.Y = np.random.normal(size=(cls.X.shape[0], 2))
def test_ols(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.X, self.Y)
# coefficient
print(self.model.coef)
print(self.model.dispersion)
print(self.model.stderr)
print(self.Y - self.model.predict(self.X))
print(self.model.loglike(self.X, self.Y))
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.02924966, -0.03484827],
[-0.00978688, 0.00336316]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.stderr,
np.array([[0.03083908, 0.03121143],
[0.03002101, 0.03038348]]).reshape(2, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185, 0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.X, self.Y),
-2758.54387369,
places=3)
# to_json
json_dict = self.model.to_json('./tests/linear_models/OLS/MultivariateOLS/')
self.assertEqual(json_dict['properties']['solver'], 'pinv')
# from_json
self.model_from_json = OLS.from_json(json_dict)
np.testing.assert_array_almost_equal(
self.model.coef,
self.model_from_json.coef,
decimal=3)
np.testing.assert_array_almost_equal(
self.model.stderr,
self.model_from_json.stderr,
decimal=3)
np.testing.assert_array_almost_equal(
self.model.dispersion,
self.model_from_json.dispersion,
decimal=3)
def test_ols_l2_regularized(self):
self.model = OLS(
solver='auto', fit_intercept=True, est_stderr=True,
reg_method='l2', alpha=0.1, l1_ratio=1, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.X, self.Y)
# coefficient
print(self.model.coef)
print(self.model.dispersion)
print(self.model.loglike(self.X, self.Y))
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.0292465, -0.03484456],
[-0.00978591, 0.00336286]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertTrue(self.model.stderr is None)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185, 0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.X, self.Y),
-2758.5438737,
places=3)
def test_ols_l1_regularized(self):
# sklearn l1 and elstic net does not support sample weight
pass
def test_ols_sample_weight_all_half(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.X, self.Y, sample_weight=0.5)
# coefficient
print(self.model.coef)
print(self.model.dispersion)
print(self.model.stderr)
print(self.model.loglike(self.X, self.Y, sample_weight=0.5))
self.assertEqual(self.model.coef.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.coef,
np.array([[-0.02924966, -0.03484827],
[-0.00978688, 0.00336316]]).reshape(2, -1),
decimal=3)
# std.err of coefficient (calibrated by df_resid)
self.assertEqual(self.model.stderr.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.stderr,
np.array([[0.03083908, 0.03121143],
[0.03002101, 0.03038348]]).reshape(2, -1),
decimal=2)
# scale
self.assertEqual(self.model.dispersion.shape, (2, 2))
np.testing.assert_array_almost_equal(
self.model.dispersion,
np.array([[0.94905363, 0.0164185],
[0.0164185, 0.89937019]]),
decimal=3)
# loglike/_per_sample
self.assertAlmostEqual(
self.model.loglike(self.X, self.Y, 0.5),
old_div(-2758.54387369, 2.),
places=3)
self.assertEqual(
self.model.loglike_per_sample(self.X, self.Y).shape,
(1000, ))
def test_ols_sample_weight_all_zero(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.assertRaises(ValueError, self.model.fit, self.X, self.Y, 0)
def test_ols_sample_weight_half_zero_half_one(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
len_half = 500
self.model.fit(self.X, self.Y,
sample_weight=np.array([1] * len_half +
[0] * (self.X.shape[0] - len_half)))
self.model_half = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model_half.fit(self.X[:len_half], self.Y[:len_half])
# coefficient
np.testing.assert_array_almost_equal(
self.model.coef,
self.model_half.coef,
decimal=3)
# std.err
np.testing.assert_array_almost_equal(
self.model.stderr,
self.model_half.stderr,
decimal=3)
# scale
np.testing.assert_array_almost_equal(
self.model.dispersion,
self.model_half.dispersion,
decimal=3)
# corner cases
def test_ols_one_data_point(self):
self.model = OLS(
solver='pinv', fit_intercept=True, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.X[0:1, :],
self.Y[0:1, ], sample_weight=0.5)
# coef
self.assertEqual(self.model.coef.shape, (2, 2))
# scale
np.testing.assert_array_almost_equal(
self.model.dispersion, np.array([[0, 0], [0, 0]]), decimal=6)
# loglike_per_sample
np.testing.assert_array_equal(self.model.loglike_per_sample(
self.X[0:1, :], self.Y[0:1, ]), np.array([0]))
np.testing.assert_array_almost_equal(self.model.loglike_per_sample(
np.array(self.X[0:1, :].tolist() * 6),
np.array([self.Y[0, ], self.Y[1, ], self.Y[0, ],
self.Y[1, ], self.Y[1, ], self.Y[0, ]])),
np.array([0, -np.Infinity, 0, -np.Infinity, -np.Infinity, 0]), decimal=3)
def test_ols_multicolinearty(self):
self.model_col = OLS(
solver='pinv', fit_intercept=False, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
X = np.hstack([self.X[:, 0:1], self.X[:, 0:1]])
self.model_col.fit(X,
self.Y, sample_weight=0.5)
self.model = OLS(
solver='pinv', fit_intercept=False, est_stderr=True,
reg_method=None, alpha=0, l1_ratio=0, tol=1e-4, max_iter=100,
coef=None, stderr=None, dispersion=None)
self.model.fit(self.X[:, 0:1],
self.Y, sample_weight=0.5)
# stderr
self.assertEqual(self.model_col.stderr, None)
# scale
np.testing.assert_array_almost_equal(
self.model_col.dispersion, self.model.dispersion, decimal=3)
# loglike_per_sample
np.testing.assert_array_almost_equal(
self.model_col.loglike_per_sample(X, self.Y),
self.model.loglike_per_sample(self.X[:, 0:1],
self.Y), decimal=0)
np.testing.assert_array_almost_equal(
self.model_col.predict(X),
self.model.predict(self.X[:, 0:1]), decimal=1)